
 The boundary condition () enforces the diffuse interface separating both fluids to always intersect the boundary \(\Gamma \)  at a perfect angle of ninety degrees. Of course, this restrictive condition will not always be satisfied in concrete applications as the contact angle of the interface might deviate from ninety degrees and even change dynamically over the course of time.
For instance, as shown in [1]}, the boundary conditions () are thus not suitable to describe moving contact line problems. This is because contact-line singularities could arise where the tangential force exerted by the fluids on the boundary around the moving contact line becomes infinite.

 The boundary condition () can be regarded as a no-flux boundary condition as it already implies \(J\cdot \mathbf {n}= 0\)  on \(\Sigma \) . Therefore, the system ((),()) can merely describe the situation where the mass of both fluids in the bulk \(\Omega \)  is conserved but it is not capable of describing a transfer of material between bulk and surface which could, for instance, be caused by absorption or adsorption processes as well as chemical reactions taking place on the boundary (see, e.g., [2]}).

